Introduction. Now the need for fresh water, both for domestic needs
and for the production enterprises, grows in many countries of the
world. Especially this problem is particularly acute in the countries of
the Arabian Peninsula and the Persian Gulf. As of 2008 the Persian Gulf
countries were producing 58% of the bulk world volume of desalinated
water. Global climate changes and population growth do a problem of
fresh water more and more urgent for the majority of regions of the
Globe [1].

Especially high requirements for the consumed water are placed by
heat power production. On nuclear power plants water is used as a
working medium and as the coolant. Effectiveness of thermal energy
transfer and the its subsequent transformation into a mechanical energy
is defined by purity of surfaces of metal contacting with water and
steam. According to technical requirements, the quantity of permeates in
working water must be no more than 10 pg/l [2].

The required quality of water can be reached only by means of
technologies of a thermal desal ting (distillation) which have several
modifications. Multistage installations of instantaneous flashing (MSF)
are mainly used in large stationary installations. In the presence of
the industrial vapor sources the installations with thermal vapour
compression (TVC) are optimum. Far from the industrial vapour sources
and in mobile installations the technology of a desalting with
mechanical vapour compression (MVC) has the greatest advantages. In this
research this technology is chosen for the detailed analysis.

In the works of El-Dessouky [3] and Al-Juwayhel et al. [4] the
mathematical models of systems with MVC are developed. Further
researches were devoted to decrease in prime cost of the water freshened
with MVC use. In particular, Lara [5, 6] investigated the prospects of
use of high performance gerotor compressors and hydrophobic
evaporators-condensers, and Cherkasskiy [7] investigated
high-temperature working modes.

The aim of this research is to identify the reserves of efficiency
increasing of the desalination systems based on mechanical vapour
compression by optimization of the scheme and parameters of
installations with MVC.

To achieve the goal, it is necessary to solve the following
problems:

--to modify and complete the mathematical model of installations
with MVC;

--increase the convergence of iterative methods and the reliability
the obtained results;

--to modify the scheme of heat exchangers plug-in;

--to research the influence of design parameters of desalination
installation on the cost of an inventory and the electric power.

Materials and Methods. The scheme of the offered desalination
installation is submitted in Fig. 1.

The main element of this installation is a uniform block of the
evaporator-condenser, or the latent heat exchanger.

Seawater after preliminary heating in heat exchangers comes to the
evaporator-condenser where receives the main heat amount from the
condensed vapour. A part of seawater evaporates, and the strong solution
of salt (brine) goes out of the evaporator, and after cooling is dumped
back in the sea. The formed vapour is compressed by the compressor and
comes to the condenser.

The T(s)--chart of process is schematically shown in Fig. 2. Here,
the piece 1-2 shows the process of evaporation of seawater;
2-3--compression of vapour in the compressor which can be considered as
adiabatic; 3-4 -isobaric cooling, 4-5--devaporation.

Essential singularity of this scheme is that condensation takes
place at higher temperature, than evaporation. Due to this the heat
evolved at devaporation is used for evaporation of seawater. Thereby in
this class of desalination installations the principle of a heat pump is
implemented.

Now let's write down a weight conservation law for water and
for salt respectively:

[G.sub.f] = [G.sub.d] + [G.sub.b], (1)

[G.sub.f][X.sub.f] = [G.sub.b][X.sub.b], (2)

where G--mass flow of substance (water, salt);

X--salt concentration.

Here indexes f, d and b belong to the feeding ocean water, the
distillate and a brine dumped in the sea respectively.

The energy balance for the device in general is calculated
according to the equation

For a numerical example is set that a mass output of distillate is
1 kg/s. The amount of heat needed to evaporate the second mass of vapour
is calculated using the formula

[Q.sub.2] = [G.sub.d][r.sub.b], (5)

where [r.sub.b]--latent heat of vaporization at boiling point of a
brine.

The quantity of heat [Q.sub.2] has to be transmitted to the boiling
brine through evaporator-condenser walls.

The temperature of vapour which is formed during salty water
boiling can be calculated as

[T.sub.v] = [T.sub.b]-BPE,

where BPE--boiling point elevation, which can be calculated
according to [3, 4].

The saturation pressure in an evaporator corresponding to
temperature [T.sub.v] is calculated by the formula

[P.sub.v] = [P.sub.s] ([T.sub.v]).

For further calculations it is necessary to set first approximation
for temperature [T.sub.d] at which the vapour in the condenser is
condensed. Further value of [T.sub.d] is defined by method of simple
iterations The compressor has to create pressure in the condenser that
would be equal to saturated vapor pressure at temperature [T.sub.d],
i.e.

[P.sub.d] = [P.sub.s] ([T.sub.d]).

Vapor pressures on the saturation line [p.sub.s] ([T.sub.d]) and
[p.sub.s] ([T.sub.b]) are also calculated according to the ratios given
in [4].

Estimation of minimum necessary intensity of vapour compression in
the compressor is made according to the equation

Cr = [P.sub.s] ([T.sub.d])/[P.sub.s] ([T.sub.b]). (6)

The specific power consumed by the compressor electric motor
according to [7] is calculated using formula

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (7)

where [v.sub.v]--specific volume of a saturated vapour at a
temperature [T.sub.v];

[gamma]--heat capacity ratio;

[eta]--compressor efficiency.

Apparently, the following ratio is fair in adiabatic process:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (8)

From here it is possible to evaluate the temperature of compressed
vapor

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The heat amount allocated during devaporation process is calculated
according to the ratio

where [r.sub.d]--latent heat of vaporization at condensation
temperature.

As calculations show, this power, as a rule, is more, than
[Q.sub.2] because of the "excess" values of [T.sub.s] arising
at adiabatic vapour compression in the compressor. Excess of power
([Q.sub.1] - [Q.sub.2]) in practice leads to boiling temperature
[T.sub.b] rise, and together with it--the rise of all other specific
temperatures.

However, in this work authors assume that excess of power is
compensated by a thermolysis to ambient medium, and process can be
considered as conservative one.

The heat transfer equation can be written as

[Q.sub.2] = [U.sub.e][A.sub.e] ([T.sub.d] - [T.sub.b]),

where [U.sub.e]--total heat transfer coefficient of the
evaporator-condenser;

[A.sub.e]--area of surface-heat transfer of evaporator-condenser.

At predefined values of A and U the condensation temperature id
determined uniquely

[T.sub.d] = [T.sub.b] + [Q.sub.1]/[U.sub.e][A.sub.e], (11)

but, because [U.sub.e] depends on temperature [3], it is necessary
the iterative refinement of [T.sub.d].

The loop body containing the equations (6 ... 11) repeats until
change of [T.sub.d] value becomes less than the preset small value.
Calculations show that the iterative cycle converges quickly.

Results and Discussion. All calculations were performed for a
hypothetical machine which mass yield of distillate is 1 kg/s. Thus, all
values of power and areas can be considered as appanage. The heat
transfer coefficient was calculated by the integral relations given in
[3, 4], and average value of it is 2.45 kW/([m.sup.2]K).

In fig. 3 the dependence of power and excess of power of the
compressor on a heat exchange surface area is shown.

From Fig. 3 it is evident that the necessary compressor power
significantly decreases at increase of a heat exchange surface area of
evaporator-condenser. The optimum ratio between these parameters can be
found based on the economic calculation.

Specific energy consumption on production of one cubic meter of
desalinated water is bound to a specific power with the ratio

W = 3.6 x N,

where W--specific consumption of the electric power, (kW x
h)/[m.sup.3];

N--specific power, kW/kg.

In Fig. 4 the dependence of specific power consumption of Won
temperature of seawater boiling at two various values of heat-transfer
coefficient in evaporator-condenser is shown.

From Fig. 4 it is evident that at increasing of boiling temperature
the specific energy consumption and the surplus of power lost are
simultaneously decrease. However, at increasing of boiling temperature
above 70 [degrees]? the speed of adjournment of a scum on device walls
sharply increases that leads to growth of operational expenses.

The system of preliminary water heating consisting of two heat
exchangers is offered.

The energy balance for the smaller heat exchanger utilizing heat of
distillate can be calculated from the equation

When all temperatures at input and output for each heat exchanger
are determined, it is possible to calculate the necessary areas of
surfaces of heat exchange. We will calculate log mean temperature
pressures according to the following ratios:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (14)

The necessary surfaces areas of heat exchange are calculated by the
formulas:

[A.sub.d] = [Q.sub.d]/[U.sub.d][DELTA][T.sup.I.sub.mb], (15)

[A.sub.b] = [Q.sub.b]/[U.sub.b][DELTA][T.sup.I.sub.mb]. (16)

The equations (12 ... 16) give the only solution in whole studied
range of temperatures and provide heating of seawater to temperature
[T.sub.b].

In Fig. 6 the dependence of the necessary surfaces areas of heat
exchange on boiling temperature is shown [T.sub.b].

From the plot it is visible that the areas of surfaces [A.sub.d]
for preliminary heat exchangers are 10 times less than the areas of
surfaces of evaporator-condenser [A.sub.b]. The area [A.sub.b] is
greatly rises at rise of boiling temperature T. Therefore, in economic
calculation the main attention needs to be paid to the cost of
evaporator-condenser.

Criterion of technical and economic optimization. As criterion of
comparison the annual given costs are accepted [8, 9]:

Then, the final expression for the variable part of given expenses
takes the form:

C = 0.1992 [C.sub.c] + [C.sub.el.]. (24)

The needs for the electric power are determined under condition of
installation operating within 22 hours a day and 360 days within a year.
During the choice of the equipment was accepted that productivity of
installation makes 25 [m.sup.3] per day.

Capital expenditure consists, mainly, of the cost of
evaporator-condenser, preliminary heat exchangers and the compressor.

As evaporator-condenser and preliminary heaters of seawater it is
expedient to use the lamellar heat exchangers differing in high
coefficient of a heat transfer. The analysis of cost of heat exchangers
shows that in approximate calculation it is possible to accept their
cost of directly proportional to surface area of heat exchange.

For typical in the studied range heat exchanger Ridan NN 41 the
surface area of heat exchange is 217.35[m.sup.2] at the price of 4806
USD [10]. Then the total cost of heat exchangers can be estimated using
the formula

[C.sub.h.e.] = 22.11 ([A.sub.e] + [A.sub.b] + [A.sub.d]).

Compressor cost [C.sub.compr.] can be averagely set to proportional
power of electric engine. According to [11] [C.sub.compr.]= 645 x
[N.sub.c].

Total capital expenditure will be

[C.sub.c] = [C.sub.h.e.] + [C.sub.compr.].

The given annual costs (17) have been calculated taking into
account the power of the compressor and the areas of heat exchange
surfaces obtained higher. Results of calculation of the specified cost
for installation with a productivity of 1 kg/s of desalinated water are
presented in Fig. 7.

The analysis of the plots shows that the minimum of the given
capital expenditure is reached at the specific area of
evaporator-condenser of 570[m.sup.2]. The electricity cost continuously
drops at increase of surface of heat exchange of evaporator-condenser
[A.sub.e]. Total annual costs decrease up to value [A.sub.e] =
1000[m.sup.2]. But at such great areas the heat exchangers have the
large weight and dimensions and therefore A needs to be limited
accordingly to transportation cost.

Conclusions. Numerical modeling has shown that in systems with
adiabatic compression of steam there are losses of power which are 26
... 29 % of the general expenses of energy. These losses can be reduced
when using advanced processes of compression of vapour along the line of
saturation, for example--at injection of water in the compressor.

Decrease in prime cost of desalinated water can be reached mainly
due to increase of efficiency of the compressor and increase of a heat
transfer coefficient of evaporator-condenser.

With the given productivity of desalination installation, the
optimum parameters of the compressor (from the economic point of view)
and evaporator-condenser can be found.

[9.] Preparation of a Feasibility Study for New Nuclear Power
Projects / International Atomic Energy Agency.--Vienna: IAEA, 2014.--125
p.

[10.] [TEXT NOT REPRODUCIBLE IN ASCII]
http://www.teploprofi.com/ceni/ ([TEXT NOT REPRODUCIBLE IN ASCII]:
25.05.2016).

[11.] [TEXT NOT REPRODUCIBLE IN ASCII] [[TEXT NOT REPRODUCIBLE IN
ASCII]] / ERSTEVAK Ltd.--[TEXT NOT REPRODUCIBLE IN ASCII]:
http://www.erstvak.com/equipment/ ([TEXT NOT REPRODUCIBLE IN ASCII]:
24.05.2016).